Hypophosphatasia is a rare inherited disease due to deficiency of tissue non-specific alkaline phosphatase, an enzyme essential for the proper formation of bones. Hypophosphatasia appears in various forms largely depending upon the age of the patient. The most severe form is diagnosed before birth and is invariably lethal. If diagnosed after birth or later in life, the survival rate improves. Even though the genetic defect is known, presently there is no effective treatment for this disease. Enobia Pharma has developed ENB-0040, a fusion protein composed of human recombinant tissue non-specific alkaline phosphatase, for the treatment of hypophosphatasia. The objective of the present clinical study is to test the long-term safety and effectiveness of ENB-0040 to treat infant stage hypophosphatasia. All of the patients in this extension study must have completed a prior clinical study of ENB-0040. The duration of treatment with ENB-0040 in the extension study will be one year. During that year, eligible infants with hypophosphatasia will receive the drug three times per week by injection under the skin. Small quantities of blood and urine will be taken at intervals to follow the progress of the treatment and to monitor for any problems. X-rays will also be used at various times to assess the progress of bone formation.